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If f(x) is a function with period 2L = 4 given on the interval (−2, 2) with (in the picture)

(a) Expansion f(x) using the Fourier series.

(b) Using the Fourier series in (c), prove that (in the picture)

1. 1
32
2
1
+
52
12
8
||
+

|2+ x, -2 < x < 0
f(x) =
2 — х
0 < x < 2

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